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slides1026 - CS 290H 26 October CS 290H 26 October Sparse...

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Unformatted text preview: CS 290H 26 October CS 290H 26 October Sparse approximate inverses, support graphs Sparse approximate inverses, support graphs Homework 2 due Mon 7 Nov. Sparse approximate inverse preconditioners Introduction to support theory Preconditioned conjugate gradient iteration Preconditioned conjugate gradient iteration x = 0, r = b, d = B-1 r 0, y = B-1 r for k = 1, 2, 3, . . . k = (y T k-1 r k-1 ) / (d T k-1 Ad k-1 ) step length x k = x k-1 + k d k-1 approx solution r k = r k-1 k Ad k-1 residual y k = B-1 r k preconditioning solve k = (y T k r k ) / (y T k-1 r k-1 ) improvement d k = y k + k d k-1 search direction Several vector inner products per iteration (easy to parallelize) One matrix-vector multiplication per iteration (medium to parallelize) One solve with preconditioner per iteration (hard to parallelize) Sparse approximate inverses Sparse approximate inverses Compute B-1 A explicitly Minimize || A B-1 I || F (in parallel, by columns) Variants: factored form of B-1 , more fill, . . Good: very parallel, seldom breaks down Bad: effectiveness varies widely A B-1 Support Graph Preconditioning Support Graph Preconditioning +: New analytic tools, some new preconditioners +: Can use existing direct-methods software-: Current theory and techniques limited CFIM: Complete factorization of incomplete matrix...
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This note was uploaded on 12/27/2011 for the course CMPSC 290h taught by Professor Chong during the Fall '09 term at UCSB.

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slides1026 - CS 290H 26 October CS 290H 26 October Sparse...

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